In designing electronic equipment used for telecommunications and especially for data processing, extensive use is made of electrical devices of a more or less complex nature which, like electrical measuring recorders or electronic circuits, operated by pulses, for example, are especially sensitive to the disturbing effects caused by electromagnetic radiation generated by other electrical circuits not part of these devices. This is why each of these electrical devices, in order to be protected against the parasitic radiation, is generally located inside a metal chassis serving as both mechanical support and as shielding for the electrical device. Usually, for a variety of reasons, a single electrical device is located inside a shielding chassis. Thus, for example, a peripheral device such as a disk reader designed to be connected to a central processing and control unit, is housed in a different shielding chassis from the one in which the CPU is located. This approach allows the operator to replace the device quickly without causing a prolonged shutdown of the CPU if it becomes defective. The electrical connection between the peripheral device and the CPU is provided by a shielded conducting cable attached at one end to the electrical circuits of the device, and is provided at its other end with a shielded connector that allows the cable to be connected to the electrical circuits of the CPU. In view of the fact that the CPU usually includes one or more printed circuit boards populated with electronic components, the shielded connector is generally of the type described and shown in U.S. Pat. No. 4,337,989, the connector including a first connecting part attached to the end of the shielded conducting cable and including an insulating body provided with recesses into which contact elements of a first type (female, for example) are inserted, the elements being connected to the conductors in the cable, the insulating body being covered with a shielding element connected electrically to the shielding of the cable, and a second connector part, mounted on one of the faces of a circuit board in the CPU, including an insulating body provided with recesses into which contact elements of a second type (male, for example) are inserted, the elements being designed to contact the contact elements of the first type when these two parts of the connector are coupled together, the contact elements of the second type being connected to circuits on the circuit board. The insulating body of the second connector part, mounted on the circuit board with its coupling face perpendicular to the plane of the board, is covered on the face opposite the one in contact with the board and on its two lateral faces adjacent to its coupling face, by a metal hood overlapping the ends of the contact elements protruding from the coupling face and forming a cavity into which the first connector part can be engaged. The hood, which thus ensures proper guidance of the first connector part during engagement, likewise shields the contact elements. To this end, the hood is provided with metal feet mounted on the conducting areas provided on one of the faces of the circuit board, the conducting areas themselves being electrically grounded. When the assembly composed of the circuit board and the second connector part is placed inside a metal shielding chassis, grounding is obtained simply by connecting these conducting areas to metal parts mounted inside the chassis, provided to support the assembly. So that the first connector part at the end of the shielded conducting cable can be engaaged with the second connector part, the chassis is provided with an opening opposite the second connector part, the opening having dimensions greater than those of the first connector part, allowing the operator to couple conveniently and with no difficulty, these two parts of the connector. In addition, the metal hood covering the second connector part is also provided with elastic conducting fingers which, when the first connector part is coupled to the second connector part, come in contact with the shielding element of the first part. This being the case, it will be apparent that when these two parts of the connector are coupled together, the shielding element and the shielding of the cable are both grounded successively through the elastic fingers, the metal hood, the conducting areas on the circuit board, the metal parts holding the board to the chassis, and finally the conductors which normally ground the chassis. This procedure requires that the circuit board include, in addition to the usual conductors employed for transmitting electrical signals or for applying electrical potentials of given values, specific conducting areas to allow the shielding hood both to be mounted securely on the board and also to be connected electrically to the chassis. However, the presence of these conducting areas has the disadvantage of taking up a relatively large area on the surface of the board, thereby making it necessary either to increase the dimensions of the board considerably, or to sharply increase the density of the other conductors mounted thereon. In addition, the conducting areas located near such other conductors pose the danger of inadvertently coming in contact with them, thereby causing a short circuit. In addition, the conducting part of the circuit that includes the shielding element of the first connector part, the elastic fingers, the metal hood, the conducting areas, and the metal parts that hold the board to the chassis is essentially in the shape of a loop that is disposed almost completely contained inside the chassis. As a result, the high-frequency parasitic electric currents which originate in the cable shielding under the influence of the electromagnetic radiation that prevails outside the chassis, on passing through the conducting part as they normally go to ground, generate electromagnetic radiation the magnitude of which increases with the area of the loop formed by the conducting part and with the frequency of the parasitic currents. The electromagnetic radiation generated inside the chassis by the conducting portion therefore poses the risk of seriously disturbing the electrical circuits the chassis is supposed to protect.